I mean. I get the airline’s side. You delaying this flight to take someone running late, well now you risk the downline flight being delayed.
If someone isn’t onboard 10 minutes prior to departure, it wasn’t meant to be. The airline will reschedule them. No point screwing the other 177 people waiting inside the plane, while you go play Captain to get that last passenger on and delay the flight for everyone else.
Our cutoff is 10 minutes. At best, I’ll tell the gate agent I’m okay with 5 prior if they are, and I’ll still get the flight blocked out on time.